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UNIVERSITY OF DUNDEE SCHOOL OF NURSING AND MIDWIFERY Numeracy help sheet number 1 Fractions A fraction is a part of a whole. For example ½ (a half) or ¼ (a quarter) The bottom number, the denominator, tells us how many equal parts the whole has been split into. The top number, the numerator, tells us how many of these parts we have. Things that you should be able to do with fractions: Simplify them Multiply them Divide them You can simplify a fraction if you can divide the top part and the bottom part by the same number. The most common are to divide by 2, 3, 5 or 10. Examples: Original 2 4 12 15 25 100 200 1000 Simplified 1 2 you can divide the top and bottom by 3, giving 4 5 you can divide the top and bottom by 5, giving 5 20 you can divide the top and bottom by 10, giving 20 100 Hint – can you do any more to the last 2? you can divide the top and bottom by 2, giving Simplify (and there may be more than one step to get it as simple as possible): Original 2 8 10 15 250 1000 30 90 66 99 Simplified you can divide the top and bottom by ___, giving you can divide the top and bottom by ___, giving you can divide the top and bottom by ___, giving you can divide the top and bottom by ___, giving you can divide the top and bottom by ___, giving Multiplying Fractions To multiply a fraction by a whole number, you just multiply the top by the number. To multiply a fraction by another fraction, multiply the tops together, and the bottoms together, then simplify Examples F1x F 2 working Giving Can this be simplified? 1 3 x3 3 3 1 1 Or just 1 1 5 x2 4 1x2 5x4 2 20 1 10 5 9 x4 7 5x4 9x7 20 63 No more Simplification Try these 1 2 x3 1 4 x1 2 Dividing Fractions To divide a fraction by another fraction, turn the second one over, and then multiply! Examples F1 ÷ 1 3 F2 ÷1 4 Turn it over 1 x4 3 1 1 2 ÷2 3 1 2 5 9 ÷4 7 5 9 Try these 1 ÷1 2 4 1 4 ÷2 3 multiply Giving 1x4 3x1 4 3 x3 2 1x3 2x2 3 4 x7 4 5x7 9x4 35 36 DECIMALS Numbers like these are all decimals: 2.5, 3.6, 1.333, 10.5 The decimal point(.) is used the distinguish the parts of the number. Numbers to the left of the decimal point are the normal counting numbers or whole numbers. Numbers to the right of the decimal point are parts of the whole number. If a number does not have a value for a column a 0 is used. The number 2.02 3.5 75.6 2050.004 Thousands Hundreds Tens Units Decimal Tenths Hundredths Thousandths point 2 0 2 . 3 5 . 7 5 6 . 2 0 5 0 0 0 4 . Now try some of these yourself 1345.76 3425 0 1 0 3 2 2 0 6 . . . 0 0 Rules and hints To multiply by 10 the decimal point is moved one place to the right. To multiply by 100 the decimal point is moved 2 places to the right. To multiply by 1000 the decimal point is moved 3 places to the right. Example 232.15 x 10 - move the decimal point to the right 1 place - 2321.5 To divide by 10 the decimal point is moved one place to the left. Example 94.1 ÷ 10 - move the decimal point to the left 1 place - 9.41 Of interest: If dividing by a number less than 1, the answer will be larger than what you started with! Try these multiplications and divisions: 345.23 x 10 16 x 100 654.12 ÷ 10 654.12 ÷ 100 0 Conversions The metric system always uses the rule of 1000 between different units, so if you know how to multiply or divide by 1000, then just use the same principles 1000 micrograms = 1 milligram 1000 milligrams = 1 gram 1000grams = 1 kilogram Examples: Convert 1456 micrograms to milligrams This is a division problem because micrograms are smaller than milligrams So divide by 1000 1456 ÷ 1000 - move decimal point 3 places to the left = 1.456 Convert 250 kilograms to grams This is a multiplication problem because kilograms are bigger than grams So multiply by 1000 250 x 1000 - move decimal point 3 places to the right = 250 000 Try these: Convert 25 grams to milligrams Convert 300 milligrams to grams (hint: you always need something in front of the decimal point) Convert 155 grams to micrograms (hint: you might find it easier to do it in 2 stages – grams to milligrams, then milligrams to micrograms)